I've recently upgraded from X2 to X3 and would like to be able to crosfade within the same take lane like you could in X2. Is there any way NOT to use comping mode when in take lane view? 

Take lanes is comping mode in my opinion.  If you are trying to cross fade between two clips in the same take lane wouldn't that make them the same take?  if they are you should probably just heal them. If for some reason you want to cross fade them and there is a comping split point between them then you can hold "shift" (I think) and you will get the ability to adjust the cross-fade between comped clips, whether they are in the same take lane or not.
 
Another way is to move one of the clips to another take lane and then overlap them and use the comping tools to split them where you would like and then adjust the cross-fade as described above.
 
If all else fails just close the take lanes and do the fade in the track view.

I really miss this ability from X2. Consider cleaning up the rhythm on a track. A word, note, snare drum or whatever is late, so you cut a little before it, scooch the early bit backwards and it's crossfaded on the head end. Then you backfill the hole on the tail end and you need a crossfade there, too. Not being able to do this in take lane view is a huge loss.

If you go back to to track view, you can get the job done there but ONLY if you don't have multiple takes, in which case it always chooses the wrong clip to crossfade against, and you have to go back down to take lanes to straighten out the crossfade mess. 


So yeah, you're crossfading on the same TAKE, but if you've shifted some part of the take time-wise, you need the crossfades to avoid pops and gaps. Make sense? 

"A word, note, snare drum or whatever is late, so you cut a little before it, scooch the early bit backwards and it's crossfaded on the head end. Then you backfill the hole on the tail end and you need a crossfade there, too."
 
You can do that in in take lanes. Use the smart tool. At the bottom of the clip, drag across the section you want to move. At the top of the clip the smart tool turns into the move tool. Make sure that snap is turned off or the selected portion will only move at snap values. After dragging the selected portion to the desired spot, place the cursor in the middle of the clip edge to slip edit the clips to overlap.
 
However, I find it to be easier to make the crossfade by adding a lane and dragging the edited portion to the new lane.
 
This particular edit is one of the many improvements in Platinum over X3.

No go. Even with the smart tool, it seems that take lanes no longer allow clips in the same lane to overlap. If you slip edit the edge of one clip onto the edge of another, it moves the edge of the 2nd clip out of the way of the first so that they don't overlap, and you can't crossfade them. 

Add a lane.
 
Or upgrade. Or go back to X2. X3 is not going to change